Question

The number of ways in which $20$ one rupee coins can be distributed among $5$ people such that each person get atleast $3$ rupees is

• A. $126$
• B. $63$
• C. $125$
• D. None of these

Answer 1

The correct option is A $126$

Given that there are $20$ coins to be distributed among $5$ people.

Also each person gets at least $3$ coins.

$\Rightarrow$ Total $=5\times 3=15$ coins.

$\therefore 15$ coins are already distributed in $1$ ways, we now have $5$ coins to be distributed between $5$ people.

$\Rightarrow x_1+x_2+x_3+x_4+x_5=5$ $,$ $x_i\ge 0$

No. of solutions is given by ${}^{n+r-1}{C}_{r-1}.$

$\Rightarrow n=5,$ $r=5$

$\therefore$ Required $={}^{5+5-1}{C}_{5-1}={}^9{C}_4=126.$

Hence the answer is $126.$